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302 



Journal of the American Mosquito Control Association Vol. 3, No. 2 



CLASSIC PAPER: ABBOTT'S FORMULA 



A METHOD OF COMPUTING THE EFFECTIVENESS OF AN 

INSECTICIDE 1 

W. S. ABBOTT 
Bureau of Entomology, United States Department of Agriculture 



In computing the effectiveness of insecticides, 
when an actual count of the living and dead 
insects in both the treated and untreated plats, 
or checks, is available, it is obvious that the 
insects which die from natural causes must be 
considered. Just what weight should be given to 
this factor, and how its value is to be determined, 
seem to vary with the individual experimenter. 

Perhaps the most common method is to sub- 
tract the percentage of dead in the check plat 
from the corresponding figure for the treated 
plat and call the remainder the effectiveness of 
the treatment. If the mortality in the check is 
very low this method may be fairly satisfactory, 
but if, for example, the check shows 50 per cent 
dead and the treated plat 98 per cent dead, then 



1 Reprinted from the Journal of Economic Entomol- 
ogy. Vol. 18, 1925, pp. 265-267. This is the second of 
a series of classic papers to be reprinted in the Journal 
of the American Mosquito Control Association, the first 
being T. D. Mulhern's 1942 paper on the New Jersey 
mosquito trap, which was reprinted in the December 
1985 issue (Vol. 1, pp. 411-418). Members wishing to 
nominate other papers for inclusion in the series 
should contact the Editor of the Journal. 

Today, more than sixty years after its publication, 
"Abbott's formula" for the adjustment of insect mor- 
tality rates is still used worldwide by workers engaged 
in insecticide trials and insecticide resistance testing. 
It is an essential tool of mosquito control workers 
everywhere, and in 1952 a table of values of "Abbott's 
correction" was published to facilitate its use (Healey, 
M. J. R. 1952. A table of Abbott's correction for 
natural mortality. Ann. Appl. Biol. 39: 211-212). Re- 
cently it has been shown that Abbott's formula can 
give biased estimates of treatment effects in experi- 
ments involving a single treatment and a single check 
(Fleming, R., and A. Retnakaran. 1985. Evaluating 
single treatment data using Abbott's formula with 
reference to insecticides. J. Econ. Entomol. 78: 1179- 
1181), but this is not a frequent situation in entomol- 
ogy. Although W. S. Abbott did his work on scale 
insects, his influence on mosquito control has been 
far-reaching and long-lasting.— L. C. Rutledge, Let- 
terman Army Institute of Research, Presidio of San 
Francisco, CA 94129-6800. 



the effectiveness, determined by this method, 
would be only 48 per cent. 

This matter of the proper evaluation of the 
check is not of great consequence when a series 
of tests is based on one check, but becomes 
highly important when experiments based on 
different checks are compared. 

For the last five years the entomologists of 
the Insecticide and Fungicide Board have been 
carrying on a rather extensive series of experi- 
ments with treatments against the San Jose 
scale, and in attempting to compare their results 
a method of computing what may be termed the 
"per cent control" has been developed. 

This method is based on the following line of 
reasoning: 

1. The difference between the percentage of 
living scales in the untreated check and the 
percentage of living scales in the treated plat 
gives the percentage of the original number ac- 
tually killed by the treatment. 

2. When a certain number of scales, as for 
example 20 per cent, is found to have died from 
natural causes, it logically follows that only 80 
per cent of the original infestation was living 
and could have been killed by the treatment 
applied. 

3. Since only 80 per cent of the insects could 
have been killed by the spray the "per cent 
control" would be determined by comparing the 
number actually killed with the number of living 
scales in the check. This may be reduced to a 
simple formula as follows: 

Let X = the per cent living in the check. 

Let Y = the per cent living in the treated plat. 

Then X - Y = the per cent killed by the 
treatment. 

And the percent killed by the treatment (X - 
Y) divided by the per cent living in the check 
(X) gives the control or expressed by an equa- 
tion, 



X- Y 
X 



x i00 = per cent control. 



The following examples show how 
method works out in actual practice. 



this 



June 1987 



Classic Paper: Abbott's Formula 



303 



Per cent living 

in check 

X 

45.0 ± 1.5 
45.0 ± 1.5 
83.8 ± 0.8 
83.8 ± 0.8 



Per cent living 
in treated plat 
Y 

19.5 ± 1.07 

2.4 ± 0.22 

30.3 ± 1.38 

3.6 ± 0.37 



Example 

1 

2 
3 
4 

The "per cent control" secured by the use of 
this formula is obviously no more accurate or 
significant than the original data on which it is 
based. It should therefore not be used until the 
reliability of the figures for the percentage of 
dead in the check and treated plats has been 
carefully considered. This can be done by com- 
puting the probable error for each set of counts 
and then determining the significance of the 
difference between the two counts. 

It is generally considered by biometricians 
that, when the difference between the results 
obtained in two experiments is more than three 
times its probable error, the results are signifi- 
cant, that is, if the quotient obtained when the 
difference is divided by its probable error is over 
three we can say that the difference is probably 
not due to chance but to the treatments applied. 

The probable errors for X, Y, and X - Y are 
given in the table above. 

These typical cases show how a high or low 
check affects the "per cent control," and it 
should be noted that when a high percentage of 



Difference 

(X-Y) 

25.5 ± 1.84 

42.6 ± 1.51 
53.5 ± 1.59 
80.2 ± .88 



Significance 

of 
Difference 

13.8 
28.2 
33.8 
91.1 



Per cent control 
X-Y 

X 

56.6 ± 2.77 

94.6 ± .52 
63.8 ± 1.67 

95.7 ± .44 



does 



efficiency is found the "per cent control" 
not materially reduce this figure. 

As far as I am aware this method has not been 
generally used by entomologists, but it seems to 
offer a reliable means for comparing results 
when several series of experiments have been 
carried on, each based on a different check. 

Mr. Philip Garman: I would like to ask 
Professor Abbott if there is any difference in the 
formulae used for computing the probable error 
by different persons experimenting with this 
kind of work. 

Mr. W. S. Abbott: I think Mr. Hartzell in a 
paper before this Society last year gave three 
different formulae, and there are different meth- 
ods. 

Mr. Philip Garman: How do you decide 
which method is the proper one to use? 

Mr. W. S. Abbott: It is up to the entomolo- 
gist to make the choice for himself. 

President A. F. Burgers: The next paper 
is by Albert Hartzell and F. H. Lathrop.